NUMERICAL APPROXIMATION OF MULTI-ORDER FRACTIONAL DIFFERENTIAL EQUATION BY GALERKIN METHOD WITH CHEBYSHEV POLYNOMIAL BASIS
OYEDEPO, T., Bello, A., Jos, A., Ayinde, A., Mohammed, T. (2024). NUMERICAL APPROXIMATION OF MULTI-ORDER FRACTIONAL DIFFERENTIAL EQUATION BY GALERKIN METHOD WITH CHEBYSHEV POLYNOMIAL BASIS. EKB Journal Management System, 15(2), 1-20. doi: 10.21608/jfca.2024.266136.1066
TAIYE OYEDEPO; Akanbi Kareem Bello; Abubakar Usman Jos; Abdullahi Muhammed Ayinde; Tomiwa Faatihat Mohammed. "NUMERICAL APPROXIMATION OF MULTI-ORDER FRACTIONAL DIFFERENTIAL EQUATION BY GALERKIN METHOD WITH CHEBYSHEV POLYNOMIAL BASIS". EKB Journal Management System, 15, 2, 2024, 1-20. doi: 10.21608/jfca.2024.266136.1066
OYEDEPO, T., Bello, A., Jos, A., Ayinde, A., Mohammed, T. (2024). 'NUMERICAL APPROXIMATION OF MULTI-ORDER FRACTIONAL DIFFERENTIAL EQUATION BY GALERKIN METHOD WITH CHEBYSHEV POLYNOMIAL BASIS', EKB Journal Management System, 15(2), pp. 1-20. doi: 10.21608/jfca.2024.266136.1066
OYEDEPO, T., Bello, A., Jos, A., Ayinde, A., Mohammed, T. NUMERICAL APPROXIMATION OF MULTI-ORDER FRACTIONAL DIFFERENTIAL EQUATION BY GALERKIN METHOD WITH CHEBYSHEV POLYNOMIAL BASIS. EKB Journal Management System, 2024; 15(2): 1-20. doi: 10.21608/jfca.2024.266136.1066

NUMERICAL APPROXIMATION OF MULTI-ORDER FRACTIONAL DIFFERENTIAL EQUATION BY GALERKIN METHOD WITH CHEBYSHEV POLYNOMIAL BASIS

Journal of Fractional Calculus and Applications
Article 3, Volume 15, Issue 2, July 2024, Page 1-20  XML PDF (955.23 K)
Document Type: Regular research papers
DOI: 10.21608/jfca.2024.266136.1066
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Authors
TAIYE OYEDEPO email orcid 1; Akanbi Kareem Bello2; Abubakar Usman Jos3; Abdullahi Muhammed Ayinde4; Tomiwa Faatihat Mohammed2
1Department of Applied Sciences, Federal College of Dental Technology and Therapy, Enugu, Nigeria
2Department of Mathematics, University of Ilorin, Ilorin, Nigeria.
3Department of Mathematics, University of Ilorin
4Department of Mathematics, University of Abuja, Abuja, Nigeria.
Abstract
The Galerkin method is a numerical technique used to approximate solutions to Partial Differential Equations (PDEs) or integral equations. To this end, this study employed the Galerkin method to address Multi-Order Fractional Differential Equations (MFDEs), utilizing Chebyshev Polynomials as the basis functions. The approach involved assuming an approximate solution using shifted Chebyshev polynomials, which was then substituted into the given problem. Subsequently, boundary conditions were applied. The residual equation, integrated over the interval of interest along with the weight function, resulted in a linear system of equations with unknown Chebyshev coefficient constants. Maple 18 was utilized to determine these unknown constants, which were then substituted back into the assumed solution to obtain the desired approximate solution. To assess the effectiveness of the proposed technique, numerical examples were solved, and the results were compared with existing literature. The comparison showcased that the suggested algorithm is not only accurate but also efficient in multi-order fractional differential equations. Tables and figures were employed to present and illustrate the obtained results.
Keywords
Chebyshev polynomials; Galerkin method; Fractional differential equations; Approximate solution
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